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Séminaire Géométrie et théorie des modèles

Horaires : Le vendredi 06 novembre 2015, 16h

Lieu : Sophie Germain, salle 1021

Counting points vs. counting extensions

Takehiko Yasuda (Osaka University - IHES)

In this talk, I will explain how to relate the two counting problems in the title by generalizing the McKay correspondence to number-theoretic base fields, that is, local fields and number fields. Over local fields, generalizing the McKay correspondence by Batyrev and Denef-Loeser, one can relate stringy invariants of quotient varieties to mass formulas of extensions of local fields. Over number fields, using the local result and a heuristic argument, one can (less tightly than in the local case) relate Manin's conjecture on rational points of Fano varieties to Malle's conjecture on extensions of number fields.

 

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